kburns/dss_beta_plane

README

Package: dss_beta_plane
URL: https://bitbucket.org/kburns/dss_beta_plane
Author: Keaton J. Burns

Overview

This package implements a direct statistical simulation (DSS) of barotropic beta-plane dynamics under a zonal average using Dedalus.

The equation set is based on the form presented in Tobias & Marston 2013: http://adsabs.harvard.edu/abs/2013PhRvL.110j4502T

Implementation

The Dedalus implementation solves for the first and second streamfunction cumulants over a 3D domain (x, y0, y1), with y in [a,b], analogous to (ξ, y, y') in the reference notation.

One dimensional functions, such as the first cumulant, are stored in a 'diagonal' representation in (y0, y1). That is, a 1D function c(z) would be stored as a 3D Dedalus field C such that,

C(x, y0, y1) = c(y0+y1-a)

In terms of Fourier coefficients,

<kx, ky0, ky1 | C> = δ(kx, 0) * δ(ky0, ky1) * <ky0 | c(y0)>

This representation allows C to be utilized as a 1D function of either y0 or y1 simply by interpolation at y1=a or y0=a, respectively.

An operator called FourierDiagonal implements spectral interpolation along the diagonal of a bivariate Fourier series, and is used to extract the local part of the second cumulant, which is then stored in the diagonal format described above. I.e. for g = Diag(f),

g(x, y0, y1) = f(x, y0+y1-a, y0+y1-a)